ELEC 423
Distribution of Power System
Load Characteristics
Load Characteristics
Distribution Feeder
Distribution Substation
Loads
Load and Load Curve
load on a power system is constantly changing.
There is no such thing as a “steady-state” load.
Load can be kW, KVAR, kVA, or A.
A load curve or profile is a plot of the variation in the
electrical load/demand versus time.
If this curve is plotted over a time period of 24 hours, it is
known as daily load curve . If its plotted for a week,
month, or a year, then its named as the weekly, monthly
or yearly load curve respectively.
Load Curves
• A load profile varies according to customer type
(typical examples include residential, commercial and
industrial), seasons (temperature, humidity) and
holidays.
• Power system utilities and designers use this information
to plan their distribution system and how much
electricity they will need to make available at any given
time.
Load Curves
Annual MW Demand for One Year 2013 (QU)
20
Demand, (MW) 18
16
14
12
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
Monthly MW Demand for the Month of September
2013 (QU)
20
18
Demand (MW)
16
14 Friday
Friday Friday Friday
12
10
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Day
LDC
A load duration curve (LDC) illustrates the variation of a certain load
in a downward form such that the greatest load is plotted in the left and
the smallest one in the right.
It is obtained by rearranging all the loads in
the load curve in descending order where the
time axis shows the time duration for which
each certain load continues.
LDC curve
There are some facts about the LDC that
can be summarized as:
1) the LDC is an arrangement of
all load levels in a descending
order of magnitude.
2) the area under the LDC
represents the energy demanded
by the system (consumed).
3) can be used in economic
dispatching, system planning
and reliability evaluation.
4) it is more convenient to deal
with than the load curve.
https://www.youtube.com/watch?v=3SqswxSflD4
Demand
Demand: The load averaged over a specific
period of time and must include the time interval
Demand interval : It is the
period over which the load is
averaged. This selected Δt
Example: The 15-minute
period may be 15 min, 30 min,
kW demand is 100 kW.
1 h, or even longer. Of course,
there may be situations where
the 15 and 30 min demands are
identical.
Maximum demand
Greatest of all demands that occur during
a specific time period. Must include demand interval,
period, and units.
Example:
The 15-minute Maximum kW demand for the
week was 100 kW.
Maximum demand
1.0 Maximum 15 min demand=0.980
0.9
0.8
0.7
Load (pu peak)
0.6
0.5 t=15min
0.4
0.3
Average daily demand=0.254
0.2
0.1
0.0
12am 2 4 6 8 10 12pm 2 4 6 8 10 12am
Time (h)
Example of a daily demand variation curve.
Average Demand
The average of the demands over a
specified period (day, week, month, etc.)
Must include demand interval,
period, and units.
Example:
The 15-minute average kW
demand for the month was
350 kW.
Diversified (Coincident demand)
Sum of demands imposed
by a group/class of
loads over a particular
period.
Must include demand interval,
period, and units.
Maximum Diversified Demand
Maximum of the sum
of demands imposed
by a group of loads
over a particular
period. ( )
Maximum Non-Diversified Demand
For a group of loads, the sum of the
individual maximum demands without any
restriction that they occur at the same time
Diversity Factor (𝑭𝑫 )
Ratio of the maximum non-diversified
demand to the maximum diversified demand.
Sum of individual maximum demands
FD
Diversified maximum demand
Di is the maximum demand of load i, disregarding time of occurrence
Dg Diversified maximum demand of group of loads
Dg D1 23n
Diversity Factor
Demand Factor (DF)
Demand factor is the ratio of the maximum demand of a
system to the total connected load (maximum demand when
all are used)
Max demand of system
DF
Total maximim connected load
Example: If a residence has equipment which would draw 6,000 W when all
equipment was drawing a full load, draw a maximum of 3,000 W in a specified
time, then the demand factor = 3,000 W / 6,000 W = 0.5
Demand Factor
Connected loads for high load density
apartment building 200m2 (Categorized
according to IEC Standard)
Demand Factor
Demand Factor
Utilization Factor
The utilization factor or use factor is the ratio of
the time that a piece of equipment is in use to the
total time that it could be in use.
Utilization Factor
Example: an oversized motor - 15 kW - drives a constant 12
kW load whenever it is on. The motor load factor is then 12/15
= 80%. The motor above may only be used for eight hours a
day, 50 weeks a year. The hours of operation would then be
8x7x50=2800 hours, and the motor utilization/use factor for a
base of 24x365=8760 hours per year would be 2800/8760 =
31.96%.
Load Factor (𝑭𝑳 )
Ratio of the average demand of any individual
customer or group of customers over a period to
the maximum demand over the same period.
Example: using a large commercial
F L
electrical bill:
peak demand = 436 kW
use = 57200 kWh
number of days in billing cycle = 30 days
→Load Factor = {57200 kWh / (30 days × 24 hours
per day × 436 kW) } × 100% = 18.22%
Load Factor
Its value is always less than one because maximum demand is always
higher than average demand, since facilities likely never operate at full
capacity for the duration of an entire 24-hour day.
The load factor is closely related to and
often confused with the demand factor.
Maximum load in a given time period Maximum demand
DF
Maximum possible load Maximum possible load
Average load
FL
Maximum load in a given time period
Load Diversity (LD)
Difference between maximum non-diversified
demand and the maximum diversified demand.
It is “the difference between the sum of the peaks
of two or more individual loads and the peak of the
combined load”.
Therefore, the load diversity (LD) is:
Diversity Factor
Max demand of system i Di
DFi
Total maximim connected load i TCDi
Di DFi * TCDi
TCDi is the total connected
demand of group, or class, i
n n
load
D i TCD DF
i i DFi is the demand factor of
FD i 1
i 1
group, or class, i load
Dg Dg
Example
Example
Example
Example
• A single-phase lateral provides service to three
• distribution transformers as shown below.
N1 N2 N3 N4
T1 T2 T3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Example
• The energy in kWh consumed by each
customer during a month is known.
T1 Custo
#1 #2 #3 #4 #5
mer
kWh 1523 1645 1984 1590 1456
T2
Custom
#6 #7 #8 #9 #10 #11
er
kWh 1235 1587 1698 1745 2015 1765
T3
Custome
#12 #13 #14 #15 #16 #17 #18
r
kWh 2098 1856 2058 2265 2135 1985 2103
Example
• A load survey has been conducted for customers in this class,
and it has been found that the customer 15-mimute maximum
kW demand is given by the equation
kWdemand 0.2 0.008 kWh
a) Determine for each transformer the 15-mimute
noncoincident maximum kW demand.
b) Using the Diversity Factor Table (next slide), determine the
15-mimute maximum diversified kW demand.
c) Determine the 15-mimute noncoincident maximum kW
demand and 15-minute maximum diversified kW demand
for each of the line segments.
Example
Diversity Factors vs
Number of Customers
N FD N FD N FD N FD N FD N FD N FD
1 1.00 11 2.67 21 2.90 31 3.05 41 3.13 51 3.15 61 3.18
2 1.60 12 2.70 22 2.92 32 3.06 42 3.13 52 3.15 62 3.18
3 1.80 13 2.74 23 2.94 33 3.08 43 3.14 53 3.16 63 3.18
4 2.10 14 2.78 24 2.96 34 3.09 44 3.14 54 3.16 64 3.19
5 2.20 15 2.80 25 2.98 35 3.10 45 3.14 55 3.16 65 3.19
6 2.30 16 2.82 26 3.00 36 3.10 46 3.14 56 3.17 66 3.19
7 2.40 17 2.84 27 3.01 37 3.11 47 3.15 57 3.17 67 3.19
8 2.55 18 2.86 28 3.02 38 3.12 48 3.15 58 3.17 68 3.19
9 2.60 19 2.88 29 3.04 39 3.12 49 3.15 59 3.18 69 3.20
10 2.65 20 2.90 30 3.05 40 3.13 50 3.15 60 3.18 70 3.20
Example
Transformer Customer # kWh kW
1 1523 12.4
a) Calculate each 2 1645 13.4
customer 15-mimute T1 3 1984 16.1
maximum kW demand 4 1590 12.9
based on the given 5 1456 11.8
equation: 6 1235 10.1
7 1587 12.9
8 1698 13.8
T2
9 1745 14.2
kWdemand 0.2 0.008 kWh 10 2015 16.3
11 1765 14.3
12 2098 17.0
13 1856 15.0
14 2058 16.7
T3 15 2265 18.3
16 2135 17.3
17 1985 16.1
18 2103 17.0
Total 265.5
Example
b) Using the Diversity Factors given in the Table and based on the number of
customers fed by each feeder and Transformer we can determine the maximum
diversified demand flowing down in each feeder and transformer as follows.
Maximum
#
Maximum Diversified
Feeder Custome FD
Load (kW) Demand
rs
(kW)
N1-N2 18 2.86 265.5 92.8
N2-N3 13 2.74 199.0 72.6
N3-N3 7 2.40 117.4 48.9
Maximum
#
Transforme Maximum Diversified
Customer FD
r Load (kW) Demand
s
(kW)
T1 5 2.20 66.6 30.3
T2 6 2.30 81.6 35.5
T3 7 2.40 117.4 48.9
Example
Example
Coincidence Factor
• Coincidence Factor
– It is “the ratio of the maximum coincident total
demand of a group of Consumers to the sum of the
maximum power demands of individual
consumers.
Diversified maximum demand Dg 1
FC n
Sum of individual maximum demands FD
i
i 1
D
Coincidence Factor
Apartments Coincidence (Simultaneity)
Factor
According to IEC Standard for
apartment block
2-4 1
5-9 0.78
10-14 0.63
15-19 0.53
20-24 0.49
25-29 0.46
30-34 0.44
35-39 0.42
40-49 0.41
50 and above 0.40
Example
Assume that there are two primary feeders
supplied by one of the three transformers
located at a distribution substation, as shown in
the Figure.
One of the feeders supplies an industrial load
that occurs primarily between 8 AM and 11
PM, with a peak of 2000 kW at 5 PM.
The other one feeds residential loads that occur
mainly between 6 AM and 12 PM, with a peak
of 2000 kW at 9 PM, as shown in next slide.
Example
Determine the following:
a) The diversity factor of
the load connected to
transformer T3.
b) The load diversity of
the load connected to
transformer T3.
c) The coincidence
(simultaneity) factor of
the load connected to
transformer T3.
Example
2
D i
2000 2000
a) The diversity factor of the load is: FD i 1
1.33
Dg 3000
b) The load diversity is: LD Di Dg 4000 3000 1000 kW
i 1
1 1
c) The coincidence factor of the load is: Fc 0.752
FD 1.33
Contribution Factor
– “ci” is the contribution factor of the ith load to the group
maximum demand. It is given in per unit of the individual
maximum demand of the ith load.
demand at time of system peak
ci
non - diversified maximum demand
Example
n
n c D i i
Dg ci Di Fc i 1
n
D
i 1
i
i 1
n
Case 1: D1 = D2 = D3 = … = Dn = D. c i
Fc i 1
n
That is, the coincidence factor is equal
Two Special Cases to the average contribution factor.
Case 2: c1 = c2 = c3 = … = cn = c. Fc c
That is, the coincidence factor is equal
to the contribution factor.
Example
Load kW
Time Street Lighting Residential Commercial Total
12AM 100 200 200 500
• Use the load curve data given in this table. 1 100 200 200 500
2 100 200 200 500
Note that the peak occurs at 5 PM. 3 100 200 200 500
• Determine the following: 4 100 200 200 500
5 100 200 200 500
a) The class contribution factors for each 6 100 200 200 500
of the three load classes 7 100 300 200 600
b) The diversity factor for the primary 8 0 400 300 700
9 0 500 500 1000
feeder
10 0 500 1000 1500
c) The diversified maximum demand of 11 0 500 1000 1500
the load group 12:00 PM 0 500 1000 1500
1 0 500 1000 1500
d) The coincidence factor of the load 2 0 500 1200 1700
group 3 0 500 1200 1700
4 0 500 1200 1700
5 0 600 1200 1800
6 100 700 800 1600
7 100 800 400 1300
8 100 1000 400 1500
9 100 1000 400 1500
10 100 800 200 1100
11 100 600 200 900
12AM 100 300 200 600
Example
a) The class contribution factor is
0 kW 1200 kW
cstreet 0 ccommertial 1.0
100 kW 1200 kW
600 kW
cresidential 0.6
1000 kW
b) The diversity factor is
3
D
i 1
i
FD 3
c D
i 1
i i
100 1000 1200
1.278
0 100 0.6 1000 1.0 1200
Example
3
c) Dg ci Di 0 100 0.6 1000 1.0 1200
i 1
1800 kW
1 1
d) Fc 0.7826
FD 1.278
Loss Factor
• Loss Factor
– It is “the ratio of the average power loss to the peak-load
power loss during a specified period of time”.
Average power loss
FLS
Power loss at peak load
Example
• Assume that the annual peak load of a primary
feeder is 2000 kW, at which the power loss
(that is total copper or ΣI2R loss) is 80 kW per
three phases.
• Assuming an annual loss factor of 0.15,
determine:
a) The average annual power loss
b) The total annual energy loss due to the
copper losses of the feeder circuits.
Example
Power loss at peak load 80kW
Average power loss
a) FLS 0.15
Power loss at peak load
Average power loss Power loss at peak load FLS
80kW 0.15
12kW
b) The total annual energy loss is:
TAELCu Average power loss 8760h/year
12 kW 8760 h
105,120 kWh
Example
• Assume that feeder 4 of the of the
distribution system in this figure has a
system peak of 3000 kVA per phase
and a copper loss of 0.5% at the
system peak.
• Determine the following:
a) The copper loss of the feeder in
kilowatts per phase.
b) The total copper losses of the
feeder in kilowatts per three
phases.
Example
a) The copper loss of the feeder in kilowatts per phase is
I 2 R 0.5% system peak
I 2 R 0.005 3000 kVA/phase 15 kW/phase
b) The total copper losses of the feeder in kilowatts per three phases is
3I 2 R 3 15 45 kW for the 3 phases
